Math 412 -- Mathematical Analysis II, MT 10:20 - 11:40AM ARC 110 ---- Spring 2018

Final Exam: Monday, May 7, 8-11am, ARC-110.

Textbook

Principles of Mathematical Analysis, by Walter Rudin, Third Edition

Office Hour

Monday 3:20--4:40pm, or by appointment

Policy

Homework 20% ; Exam 1 20%; Exam 2 20%; Final Exam 40% (No late homework, drop two lowest for homework)

Extra meeting time

Once a week. Will use one of the following time and place: Friday, 1:40-3pm, Hill 525; Wed. 10:30--11:50am, Hill 705; Tuesdat, 1:40-3pm, Hill 705

Syllabus and homework

Date Section Homework

Jan. 18 Chapter 7, Sequences of Functions: Examples, Issues, and Uniform Convergence Homework to be handed in: Page 165, #2,3, 4,6. Homework not handed in: Page 176, #1,5,7 --- these I will go over on Jan. 23, Tuesday, 1:40-3pm, Hill 705.

Jan. 22 Chapter 7, Uniform convergence and continuity, Uniform convergence and integration, Homework to be handed in: Page 166-167, #9, 11. Homework not handed in: P166, #8.
Extra Meeting Time: Jan. 23, Tuesday, 1:40-3pm, Hill 705.

Jan. 25 Chapter 7, Uniform convergence and differentiation Homework to be handed in: Page 166, #7, 8.
Extra Meeting Time: Jan. 31, Wed. 10:30-11:50am, Hill 705.

Jan. 29 Chapter 7, Equicontinuity Homework to be handed in: Page 167-168, #13, 15. Homework not handed in: Page 168, #16, 17, 19

Feb. 1 Chapter 7, Equicontinuity and Stone-Weisstrass Theorem Homework to be handed in: page 168-169, #16, 20. Homework not handed in: Page 169, #23.
Extra Meeting Time: Feb. 5, Monday, 3:20-4:40pmpm, Hill 705.

Feb. 5 Chapter 8, Power Series, Abel's theorem, Homework to be handed in: Page 196, #1, 3. Homework not handed in: Page 196, #2.

Feb. 8 Chapter 8, Exponential and Logarithmic functions, Trigonomic functions Homework to be handed in: Page 196, 4a, 4c, 5a, 5c. Homework not handed in: Page 197, #6, #4b, 4d, 5b, 5d.

Feb. 12 Chapter 8, Algebraic completeness of the complex field, Fourier Series Homework to be handed in: Page 197, #7, Page 198, #12(a), Homework not handed in: Page 197, #8.

Feb. 15 Chapter 8, Fourier Series Homework to be handed in: Page 198, #12(b), 12(c), 12(d), 12(e), Page 199, #14. Homework not handed in: Page 198, #13.

Feb. 19 Chapter 6, Riemann-Stieltjes integrals, definition and existence of the integral Homework to be handed in: Page 138, #1, #4. Homework not handed in: Page 138, #2, 3, 5, 7.

Feb. 22 Exam #1
(Homework to be handed in: Page 138, #5, 7)

Feb. 26 Chapter 6, Properties of the integral Homework to be handed in: Page 138, #3, 8. Homework not handed in: Page 138-139, #6, 9, 10, 11.
Extra Meeting Time: March 5, Monday, 3:30-4:40pm, Hill 705.

March 1 Chapter 6, Properties of integrals Homework to be handed in: Page 139, #9, 10. Homework not handed in: Page 140, #11, 12.

March 5 Chapter 6, Integration and differentiation, Rectifiable curves Homework to be handed in: Page 140-141, #18, 15. Homework not handed in: Page 141-142, #17, 19.

March 8 Chapter 9, Linear transformations Homework to be handed in: Page 239, #3, 5. Homework not handed in: Page 239, #1, 2, 4.

March 19 Chapter 9, Differentiation Homework to be handed in: Page 239-240, #7, 11, 14. Homework not handed in: Page 239-240, #6, 9, 10, 12, 13.

March 22 Chapter 9, The contraction principle, the Inverse Function Theorem Homework to be handed in: Page 239-240, #15, 17. Homework not handed in: Page 239-240, #8, 13, 14, 16.

March 26 Chapter 9, The Implicit Function Theorem Homework to be handed in: Page 241-242, #19, 21. Homework not handed in: Page 241-242, #20, 22, 23.
Make-up Office Hour: March 27, Tuesday, 1:40-3:20pm, Hill 702.

March 29 Chapter 9, The Implicit Function Theorem,Derivatives of higher order, Differential of integrals Homework to be handed in: Page 242, #26, 28. Homework not handed in: Prepare for Exam 2.

April 2 Chapter 10. Integration of Differential Forms Homework not handed in: Prepare for Exam 2.

April 5 Exam #2

April 9 Chapter 10, Integration, Primitive Mappings, Partition of Unity Homework to be handed in: Page 288, #2, 4. Homework not handed in: Page 288, #1, 3.

April 12 Chapter 10, Partition of Unity, Change of Variable,s, Differential Forms Homework to be handed in: Page 290, #9, 11.

April 16 Chapter 10, Differential Forms Homework to be handed in: Page 291-294, #15, 22. Homework not handed in: Page 290-293, #12, 13, 21.

April 19 Chapter 10, Simplexes and Chains, Stokes' Theorem, Closed Forms and Exact Forms Homework to be handed in: Page 290-292, #17, 20, 24. Homework not handed in: Page 290-292, #16, 18, 19, 23.

April 23 Chapter 10, Poincare Lemma, Vector Analysis Homework handed in: Page 297, #28.

April 26 Chapter 10, Vector Analysis, partial review Prepare for the Final Exam
Extra Meeting Time: May 2, Wed, 1:40-3:20pm, Hill 702.

April 30 Partial review Prepare for the Final Exam

Date	Section	Homework
Jan. 18	Chapter 7, Sequences of Functions: Examples, Issues, and Uniform Convergence	Homework to be handed in: Page 165, #2,3, 4,6. Homework not handed in: Page 176, #1,5,7 --- these I will go over on Jan. 23, Tuesday, 1:40-3pm, Hill 705.
Jan. 22	Chapter 7, Uniform convergence and continuity, Uniform convergence and integration,	Homework to be handed in: Page 166-167, #9, 11. Homework not handed in: P166, #8. Extra Meeting Time: Jan. 23, Tuesday, 1:40-3pm, Hill 705.
Jan. 25	Chapter 7, Uniform convergence and differentiation	Homework to be handed in: Page 166, #7, 8. Extra Meeting Time: Jan. 31, Wed. 10:30-11:50am, Hill 705.
Jan. 29	Chapter 7, Equicontinuity	Homework to be handed in: Page 167-168, #13, 15. Homework not handed in: Page 168, #16, 17, 19
Feb. 1	Chapter 7, Equicontinuity and Stone-Weisstrass Theorem	Homework to be handed in: page 168-169, #16, 20. Homework not handed in: Page 169, #23. Extra Meeting Time: Feb. 5, Monday, 3:20-4:40pmpm, Hill 705.
Feb. 5	Chapter 8, Power Series, Abel's theorem,	Homework to be handed in: Page 196, #1, 3. Homework not handed in: Page 196, #2.
Feb. 8	Chapter 8, Exponential and Logarithmic functions, Trigonomic functions	Homework to be handed in: Page 196, 4a, 4c, 5a, 5c. Homework not handed in: Page 197, #6, #4b, 4d, 5b, 5d.
Feb. 12	Chapter 8, Algebraic completeness of the complex field, Fourier Series	Homework to be handed in: Page 197, #7, Page 198, #12(a), Homework not handed in: Page 197, #8.
Feb. 15	Chapter 8, Fourier Series	Homework to be handed in: Page 198, #12(b), 12(c), 12(d), 12(e), Page 199, #14. Homework not handed in: Page 198, #13.
Feb. 19	Chapter 6, Riemann-Stieltjes integrals, definition and existence of the integral	Homework to be handed in: Page 138, #1, #4. Homework not handed in: Page 138, #2, 3, 5, 7.
Feb. 22	Exam #1 (Homework to be handed in: Page 138, #5, 7)
Feb. 26	Chapter 6, Properties of the integral	Homework to be handed in: Page 138, #3, 8. Homework not handed in: Page 138-139, #6, 9, 10, 11. Extra Meeting Time: March 5, Monday, 3:30-4:40pm, Hill 705.
March 1	Chapter 6, Properties of integrals	Homework to be handed in: Page 139, #9, 10. Homework not handed in: Page 140, #11, 12.
March 5	Chapter 6, Integration and differentiation, Rectifiable curves	Homework to be handed in: Page 140-141, #18, 15. Homework not handed in: Page 141-142, #17, 19.
March 8	Chapter 9, Linear transformations	Homework to be handed in: Page 239, #3, 5. Homework not handed in: Page 239, #1, 2, 4.
March 19	Chapter 9, Differentiation	Homework to be handed in: Page 239-240, #7, 11, 14. Homework not handed in: Page 239-240, #6, 9, 10, 12, 13.
March 22	Chapter 9, The contraction principle, the Inverse Function Theorem	Homework to be handed in: Page 239-240, #15, 17. Homework not handed in: Page 239-240, #8, 13, 14, 16.
March 26	Chapter 9, The Implicit Function Theorem	Homework to be handed in: Page 241-242, #19, 21. Homework not handed in: Page 241-242, #20, 22, 23. Make-up Office Hour: March 27, Tuesday, 1:40-3:20pm, Hill 702.
March 29	Chapter 9, The Implicit Function Theorem,Derivatives of higher order, Differential of integrals	Homework to be handed in: Page 242, #26, 28. Homework not handed in: Prepare for Exam 2.
April 2	Chapter 10. Integration of Differential Forms	Homework not handed in: Prepare for Exam 2.
April 5	Exam #2
April 9	Chapter 10, Integration, Primitive Mappings, Partition of Unity	Homework to be handed in: Page 288, #2, 4. Homework not handed in: Page 288, #1, 3.
April 12	Chapter 10, Partition of Unity, Change of Variable,s, Differential Forms	Homework to be handed in: Page 290, #9, 11.
April 16	Chapter 10, Differential Forms	Homework to be handed in: Page 291-294, #15, 22. Homework not handed in: Page 290-293, #12, 13, 21.
April 19	Chapter 10, Simplexes and Chains, Stokes' Theorem, Closed Forms and Exact Forms	Homework to be handed in: Page 290-292, #17, 20, 24. Homework not handed in: Page 290-292, #16, 18, 19, 23.
April 23	Chapter 10, Poincare Lemma, Vector Analysis	Homework handed in: Page 297, #28.
April 26	Chapter 10, Vector Analysis, partial review	Prepare for the Final Exam Extra Meeting Time: May 2, Wed, 1:40-3:20pm, Hill 702.
April 30	Partial review	Prepare for the Final Exam